A well known positioning system which is based on the evaluation of signals transmitted by beacons is GPS (Global Positioning System). The constellation in GPS consists of more than 20 satellites employed as beacons that orbit the earth. The distribution of these satellites ensures that usually between five and eight satellites are visible from any point on the earth.
Each of the satellites, which are also called space vehicles (SV), transmits two microwave carrier signals. One of these carrier signals L1 is employed for carrying a navigation message and code signals of a standard positioning service (SPS). The L1 carrier phase is modulated by each satellite with a different C/A (Coarse Acquisition) Code. Thus, different channels are obtained for the transmission by the different satellites. The C/A code, which spreads the spectrum over a 1 MHz bandwidth, is repeated every 1023 bits, the epoch of the code being 1 ms. The carrier frequency of the L1 signal is further modulated with navigation information at a bit rate of 50 bit/s, which information comprises in particular ephemeris data. Ephemeris parameters describe short sections of the orbit of the respective satellite. Based on these ephemeris parameters, an algorithm can estimate the position and the velocity of the satellite for any time of about 2-4 hours during which the satellite is in the respective described section. Ephemeris data also comprise clock correction parameters which indicate the current deviation of the satellite clock versus a general GPS time.
Further, a time-of-week (TOW) count is reported every six seconds as another part of the navigation message.
A GPS receiver of which the position is to be determined receives the signals transmitted by the currently available satellites, and a tracking unit of the receiver detects and tracks the channels used by different satellites based on the differently comprised C/A codes. The receiver first determines the time of transmission of the ranging code transmitted by each satellite. Usually, the estimated time of transmission is composed of two components. A first component is the TOW count extracted from the decoded navigation message in the signals from the satellite, which has a precision of six seconds. A second component is based on counting the epochs and chips from the time at which the bits indicating the TOW are received in the tracking unit of the receiver. The epoch and chip count provides the receiver with the milliseconds and sub-milliseconds of the time of transmission of specific received bits. A detected epoch edge also indicates the code phase of a received signal.
Based on the time of transmission and the measured time of arrival (TOA) of the ranging code at the receiver, the time of flight (TOF) required by the ranging code to propagate from the satellite to the receiver is determined. By multiplying this TOF with the speed of light, to the distance between the receiver and the respective satellite is obtained. The computed distance between a specific satellite and a receiver is called pseudo-range, because the general GPS time is not accurately known in the receiver. Usually, the receiver calculates the accurate time of arrival of a ranging code based on some initial estimate, and the more accurate the initial time estimate is, the more efficient are position and accurate time calculations. A reference GPS time can, but does not have to be provided to the receiver by a network.
The computed distances and the estimated positions of the satellites then permit a calculation of the current position of the receiver, since the receiver is located at an intersection of the pseudo-ranges from a set of satellites. In order to be able to compute a position of a receiver in three dimensions and the time offset in the receiver clock, the signals from four different GPS satellite signals are required.
If navigation data are available on one of the receiver channels, the indication of the time of transmission comprised in a received signal can also be used in a time initialization for correcting a clock error in the receiver. In GPS, an initial time is needed for the positioning. For the initial time estimate, the average propagation time of satellite signal of around 0.078 seconds is added to the time of transmission of a ranging code extracted from the navigation information. The result is used as initial estimate of the time of arrival of a ranging code, which estimate lies within around 20 ms of the accurate time of arrival. The receiver then determines for different satellites the time at which a respective ranging code left the satellite. Using the initial estimate of the current time, the receiver forms pseudorange measurements as the time interval during which the respective ranging code was propagating from the satellite to the receiver either in seconds or in meters by scaling with the speed of light. After the position of the receiver has been calculated from the determined pseudoranges, the accurate time of arrival can then be calculated from standard GPS equations with an accuracy of 1 μs.
However, in order to be able to make use of such a time initialization, the navigation data from a satellite signal is needed. Currently, most of the GPS receivers are designed for outdoor operations with good signal levels from satellites. Thus, only good propagation conditions ensure that the navigation data required for the described time initialization is available.
In bad propagation conditions, in contrast, it may not be possible to extract the navigation message accurately enough from received satellite signals, since a high bit-error rate and weak signal levels make a robust decoding of navigation bits impossible. Such bad propagation conditions, which are often given indoors, render the time initialization and the pseudorange measurements more difficult.
For those cases in which the standard time initialization methods cannot be applied since the navigation data are noisy, the time initialization process for the receiver can be performed by a time recovery method. Details of a time recovery method have been presented for example in “Possibilities for GPS Time Recovery with GSM Network Assistance”, Proceedings of the ION GPS 2000, September 2000, by Syrjärinne J. Such methods, however, usually require a reference position for the receiver.